Staphylococcus aureus is a pathogenic bacterium-contaminating milk and milk products causing food poisoning primarily due to its enterotoxins. The study aimed at estimating the prevalence of S. aureus in milk and milk products, assessing potential risk factors for contamination, and determining the load and the antimicrobial susceptibility profile of the isolates. A cross-sectional study design was employed to collect a total of 486 samples, comprising 383 raw milk, 47 bulk tank milk, 29 curd milk (Ergo), and 28 Ethiopian cottage cheese (Ayib) samples. Enumeration, isolation, and identification of S. aureus were carried out following standard microbiological techniques. Antibiogram was performed using 12 antimicrobials following the Kirby–Bauer disc diffusion method. Logistic regression analyses were used to assess the association between the occurrence of S. aureus in milk and milk products and potential risk factors. The overall prevalence of S. aureus was 10.69% (52/486) [95% confidence interval (CI):8.09–13.79%]. The prevalence of S. aureus in raw milk, curd milk, bulk tanks at the farm, bulk tanks at milk collection facilities, and cottage cheese was 8.64%, 24.14%, 14.73%, 23.08%, and 14.29%, respectively. The rate of isolation of S. aureus was significantly high in curd milk than in other types of samples (P = 0.010). The study revealed that teat washing (OR: 4.93, 95% CI: 2.06–11.81), use of towel (OR: 12.13, 95% CI: 3.74–39.29), and tick infestations (OR: 4.31, 95% CI: 1.28–14.44) were risk factors associated with the occurrence of S. aureus in milk. About 48.39% of the milk samples assessed had the S. aureus count higher than 105 CFU/ml. The highest rate of resistance was observed to ampicillin (95%), amoxicillin (95%), oxacillin (87.5%), and cefotaxime (80%). All isolates are resistant to at least two classes of antimicrobial drugs, while 65.0% of the isolates were found to be multidrug-resistant. The moderate prevalence, high load, and antimicrobial resistance of S. aureus indicate the higher public health risk due to the widespread consumption of raw milk in the area. Good hygienic practices, regular surveillance of antimicrobial resistance, and prudent use of drugs are suggested.